Hamiltonian (REF ) hosts topological edge states under the open boundary condition.
For finite \(\gamma \)  and \(\phi \notin \lbrace 0,\pi \rbrace \) , all eigenstates accumulate to the boundaries under the non-Hermitian skin effect. As demonstrated in Ref. [1]}, this can be understood in the limit \(\Delta ,\gamma \gg J_s,J_p,J_t\) , when Hamiltonian (REF ) can be perturbatively reduced to a non-Hermitian Su-Schrieffer-Heeger model with asymmetric hopping. Physically, this is because the interplay of the synthetic flux and on-site loss gives rise to a non-reciprocal flow along the chain. Beyond such a limit, the dissipative AB chain is qualitatively different from a non-Hermitian Su-Schrieffer-Heeger model, particularly for the lack of chiral symmetry. Nevertheless, both the non-Hermitian skin effect and band topology persist as salient features of the dissipative AB chain.
